AN INTRODUCTION TO GENERAL RELATIVITY

By R. JOMIN

CONTENTS INTRODUCTION GENERAL CONCEPTS SOME BASIC NOTIONS THE EQUIVALENCE PRINCIPLE INERTIAL FORCES THE WAKE OF NON-TRIVIAL METRIC TOWARDS GEOMETRY GEOMETRY DI?ERENTIAL GEOMETRY SPACES VECTOR AND TENSOR FIELDS DI?ERENTIAL FORMS METRICS PSEUDO-RIEMANNIAN METRIC THE NOTION OF CONNECTION THE LEVI–CIVITA CONNECTION CURVATURE TENSOR BIANCHI IDENTITIES EXAMPLES DYNAMICS GEODESICS THE MINIMAL COUPLING PRESCRIPTION EINSTEIN’S FIELD EQUATIONS ACTION OF THE GRAVITATIONAL FIELD NON-RELATIVISTIC LIMIT ABOUT TIME, AND SPACE TIME RECOVERED SPACE EQUIVALENCE, ONCE AGAIN MORE ABOUT CURVES GEODESIC DEVIATION GENERAL OBSERVERS TRANSVERSALITY FUNDAMENTAL OBSERVERS AN ASIDE: HAMILTON-JACOBI SOLUTIONS TRANSFORMATIONS SMALL SCALE SOLUTIONS THE SCHWARZSCHILD SOLUTION LARGE SCALE SOLUTIONS THE FRIEDMANN SOLUTIONS DE SITTER SOLUTIONS TETRAD FIELDS TETRADS LINEAR CONNECTIONS LINEAR TRANSFORMATIONS ORTHOGONAL TRANSFORMATIONS CONNECTIONS, REVISITED BACK TO EQUIVALENCE TWO GATES INTO GRAVITATION GRAVITATIONAL INTERACTION OF THE FUNDAMENTAL FIELDS MINIMAL COUPLING PRESCRIPTION GENERAL RELATIVITY SPIN CONNECTION APPLICATION TO THE FUNDAMENTAL FIELDS SCALAR FIELD DIRAC SPINOR FIELD ELECTROMAGNETIC FIELD GENERAL RELATIVITY WITH MATTER FIELDS GLOBAL NOETHER THEOREM ENERGY–MOMENTUM AS SOURCE OF CURVATURE ENERGY–MOMENTUM CONSERVATION